Derivation of the Equation of Caustics for the Experimental Assessment of Distributed Contact Loads with Friction in Two Dimensions

The stress-optical method of caustics is an experimental technique that can yield valuable data to assess the stress-state in the vicinity of a singularity such as the point at which a concentrated load acts or the tip of a static or a propagating crack. The present work aims to develop a mathematical background, which can be used to evaluate the complex shapes of the singular surfaces of the caustics produced from the Hertzian load distribution at the contact area between two sliding elastic bodies in order to derive the magnitude of the load and the prevailing mean coefficient of friction. The theoretical caustics are calculated numerically and plotted for various values of the coefficient of friction and experimental evidence supporting the validity of the analysis is given.